Sprinting predictive simulation - Opinions for performance based cost function

[Nicos Haralabidis]

Hello everyone,

I am trying to perform predictive simulations of sprinting whereby I am constraining the model states at the initial mesh point (match with initial states from tracking simulation), constraining the horizontal pelvis displacement at the final mesh point (match the displacement from tracking simulation) and manually adjusting the overall time horizon (with respect to the total to complete two steps from experimental data). I would of course like the resulting kinematics/GRFs to resemble those obtained from sprinting, and I was wondering whether anyone had any experience with choosing a performance based cost function that resulted in the output still resembling sprinting?

My initial thoughts were to explore maximising external centre of mass power and/or contractile element power. The use of contractile element power seems tricky due to the potential of positive and negative power, although I guess it is no different to having negative external power.

Within my current simulations I have muscle activations squared as the effort term, and I have included tracking of the relative joint kinematics, somewhat similar approach to van den Bogert et al. (2012), so the resulting kinematics are 'plausible'. I am yet to run the simulation with the kinematics tracking weight set to zero - I suspect the result will be awful as my current effort term does not capture the task of sprinting.

Any thoughts and suggestions are greatly appreciated!

PS... sorry for the length of the message!

Van den Bogert, A. J., Hupperets, M., Schlarb, H., & Krabbe, B. (2012). Predictive musculoskeletal simulation using optimal control: effects of added limb mass on energy cost and kinematics of walking and running. Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology, 226(2), 123-133.

Kind regards,

Nicos

[Ton van den Bogert]

Nicos,

Since the goal of sprinting is maximum speed or minimum time, data tracking should probably be avoided.

I have optimized a periodic sprinting cycle by simply using "-V" as the cost function, where V is the speed. I added speed V and cycle duration T as unknowns in the optimization problem. Not sure if Moco has that capability. Alternatively, you can maximize Xpelvis/T which is the same as speed, if Xpelvis=0 at the start of the cycle. Ideally, T would be optimized because you don't want to assume a certain cycle duration.

Your suggestion of maximizing power would not work because a significant amount of energy is lost in ground contact.

This was presented at ISB 2009: https://media.isbweb.org/images/conf/20 ... df/577.pdf

Air drag is important during sprinting, so you should include that in the model, unless you want to simulate sprinting on a treadmill. You can approximate air drag by a force applied to the trunk center of mass, or pelvis, proportional to velocity squared. You can find coefficients based on wind tunnel tests (e.g. Quinn, J Sports Sci 2004).

There was never a full paper because the predictions failed to replicate some important experimental results on sprinting with a prosthesis.

Ton van den Bogert

[Ross Miller]

Cycle time can be optimized but Moco doesn't have a "maximum speed" cost function (yet?), so I think predictively simulating sprinting will be hard. Some potential work-arounds could be (I haven't tried either of these):

- Average speed can be set as a constraint, so you could perform simulations with faster and faster target speeds until the model can no longer meet the constraint.

- I've thought about setting up a tracking problem where the target data is the pelvis moving at an impossibly fast speed and minimizing that tracking error.

CE power can be minimized with MocoOutputGoal, but I don't think you can negate it or square it (so it will encourage lots of negative power) and you need a separate goal for each muscle, so it's pretty slow if you want to minimize the power for all muscles in a model with lots of muscles.

I tried some predictive simulations of sprinting when I first started using direct collocation (not in Moco). The model did strange things like heel-striking and extreme angles of trunk lean that I couldn't quickly resolve, and haven't pursued it further.

Ross

[Nicos Haralabidis]

Thank you both for your prompt replies! I should have mentioned in my previous message that I am doing these simulations without Moco! I opted to post here as its an active community in the direct collocation methods world.

Professor van den Bogert, could you please elaborate on how you included V as a variable? Or was V the COM velocity of the model used in the conference proceeding you shared? and therefore calculated from the model states. I am not sure I follow its inclusion. Could you also please elaborate on the periodicity constraint you implemented in the conference proceeding?
x(T) = x(0) + V*T*x_hat; My interpretation is that for all states, except horizontal translation, they are equal at the initial and final points; periodic. Whilst for horizontal translation, the final position state variable must equal the initial position variable plus the product of (average) V and total time T.

Thank you for the air drag suggestion - we have already accounted for this aspect.

Professor Miller, I really like the suggestions regarding the constraining of the average speeds and the idea of creating artificial data to track. I will try these points!

I noticed in your article titled 'Optimal footfall patterns for cost minimization in running' (2015) that in one of the cost functions you explored minimising the contractile element power, and you mention in the supplementary material 'No distinction was made between the 'energetic fate' of eccentric vs concentric work in this calculation, which is contentious (Schmidt-Nelson, 1972'. I have tried to read the article cited to understand what is contentious, but I am still uncertain, could you please perhaps clarify?

Thanks,

Nicos

[Ross Miller]

Hi Nicos,

In those 2015 simulations we were minimizing the integral of the squared CC power, summed over all muscles (I omitted the squaring part from the description unfortunately). For this cost function the ideal result would have been zero instantaneous power at all timepoints.

The contention over "negative" work (work done on the muscle/fiber) is over how much energy this works costs and whether this work can/should be treated as a source of energy for producing positive work. I say "no" on the latter because I think it implies negative work can do things like reverse the crossbridge cycle or absorb heat. There may be recent developments that have clarified some of this, I haven't looked into it recently.

Ross

[Nicos Haralabidis]

Hello again Professor Miller,

Thank you for clarifying that the 'squaring' was missing in the supplementary material - that makes much more sense to me now (I think...!). I guess the minimization of CC power (irrespective of positive/negative) in your article leads to more efficient use of the passive in series component?

After rereading the article by Schmidt-Nelson (1972) along with the book by Winter (2009) I think I am starting to appreciate the contentious issue! Your point also helps me to further understand why in the article I cited in my first message, by Professor van den Bogert, the integral of positive CC power is considered as an outcome measure (and not both positive and negative CC power).

Lots to think about

Thanks again!

Nicos Haralabidis